Problem: Simplify the following expression: $x = \dfrac{-16n^3}{52n^2}$ You can assume $n \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-16n^3 = - (2\cdot2\cdot2\cdot2 \cdot n \cdot n \cdot n)$ The denominator can be factored: $52n^2 = (2\cdot2\cdot13 \cdot n \cdot n)$ The greatest common factor of all the terms is $4n^2$ Factoring out $4n^2$ gives us: $x = \dfrac{(4n^2)(-4n)}{(4n^2)(13)}$ Dividing both the numerator and denominator by $4n^2$ gives: $x = \dfrac{-4n}{13}$